where \({\rm n}=ck/\omega \)  is the refractive index. Therefore the eigenvalues and eigenvectors of the in–plane permittivity tensor determine the polarization and refractive index of the wave, respectively. Interestingly, Eq. (REF ) is equivalent to the Schrödinger equation for a spin \(1/2\)  particle in a magnetic field (see e.g. [1]}). With this in mind we re–write the in–plane permittivity tensors in terms of the Pauli spin matrices, \({\sigma }=\sigma _{x}{e}_{x}+\sigma _{y}{e}_{y}+\sigma _{z}{e}_{z}\) , as follows
\(\left(\begin{matrix}\epsilon _{xx}&\epsilon _{xy}\\\epsilon _{yx}&\epsilon _{yy}\end{matrix}\right)=\left(\begin{matrix}V_0+V\,\cos (\theta )&V\,\sin (\theta )\,{\rm e}^{-{\rm i}\phi }\\V\,\sin (\theta )\,{\rm e}^{{\rm i}\phi }&V_0-V\,\cos (\theta )\end{matrix}\right)=V_0{1}+V\,{n}\cdot {\sigma }.\) 
